What does partial (non-maximum) quantum entanglement mean? When quantum systems are entangled, they have a "grade of entanglement" which can be quantified e.g. as the entropy of entanglement. There also are states of "maximum entanglement", e.g. the Bell states.
But what does it mean practically if quantum systems are less than maximum entangled, e.g. with half of the maximum entropy? Does it mean that there is a probability of 50% that the systems are (maximum) entangled? Or that they will decide in the moment of measurement with a 50:50 chance to behave like maximum entangled or non-entangled? Or does it mean something else?
Or in other words: If an observable is measured for two pairs of identical particles under the same conditions, except that the first pair is maximum entangled and the second pair less the maximum entangled, what will be the difference in the measurement results?
(A similar question was already asked in a comment here by Passiday on May 24 '13 6:18, but not really answered.)
[Edit: bolded the second, better version of the question.]
 A: For an illustrative example, suppose the state space of a single particle is two-dimensional, say with orthogonal basis $X,Y$.
Now consider a two-particle system in the pure state
$$\alpha X\otimes X+\beta X\otimes Y +\gamma Y\otimes X+\delta Y\otimes Y$$
with $\alpha^2+\beta^2+\gamma^2+\delta^2==1$.
This state is called maximally entangled if $\alpha^2+\gamma^2=\beta^2+\delta^2=1/2$ and $\alpha\beta+\gamma\delta=0$.  (Exercise:  This condition is independent of the chosen basis.)
This defines maximal entanglement for a pure state.  One can extend the definition to mixed states, but there's already enough here to answer your question.  A pure state can be non-maximally entangled, therefore a non-maximally entangled state need not be non-trivially mixed, therefore no, 
a non-maximally entangled  state need not have any non-zero probability of being maximally entangled.  
As far as the rest, if your model calls for a collapse at the moment of measurement, then if you measure the first particle and find that it's in an eigenstate $Z=pX+qY$ of your measurement, then you can see that the two-pair system collapses into a state of the form $Z\otimes W$, which is not entangled at all (regardless of whether it was maximally or non-maximally entangled to begin with).
